Kirsty Hanson's late double ensured the margin of victory was comfortable in the end, but it was far from plain sailing in the first half when Jane Ross's opener for the Reds was overturned with a strike from Walker and then an own goal by Abbie McManus.
United captain Katie Zelem levelled the score at 2-2 for half-time with a free-kick, after former team-mate Mollie Green fouled Ella Toone. And when Toone later made it 3-2, Casey Stoney's side were able to stretch ahead and add those two further goals from Hanson.
Picking up all three points was the perfect way to build on last weekend's promising opener when the Reds held reigning WSL champions Chelsea to a hard-fought 1-1 draw at Leigh Sports Village.